CA1321495C - Diffraction grating and manufacturing method thereof - Google Patents
Diffraction grating and manufacturing method thereofInfo
- Publication number
- CA1321495C CA1321495C CA000587161A CA587161A CA1321495C CA 1321495 C CA1321495 C CA 1321495C CA 000587161 A CA000587161 A CA 000587161A CA 587161 A CA587161 A CA 587161A CA 1321495 C CA1321495 C CA 1321495C
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- Prior art keywords
- photosensitive layer
- theta
- groove
- substrate
- gamma
- Prior art date
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Classifications
-
- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
-
- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B5/00—Optical elements other than lenses
- G02B5/18—Diffraction gratings
- G02B5/1847—Manufacturing methods
- G02B5/1857—Manufacturing methods using exposure or etching means, e.g. holography, photolithography, exposure to electron or ion beams
-
- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B5/00—Optical elements other than lenses
- G02B5/18—Diffraction gratings
- G02B5/1861—Reflection gratings characterised by their structure, e.g. step profile, contours of substrate or grooves, pitch variations, materials
Abstract
ABSTRACT OF THE DISCLOSURE
A diffraction grating has a reflection film formed on a photosensitive layer disposed on a substrate through exposure followed by development and the groove profile thus formed has a configuration distorted from a sinusoidal form because the sensitivity curve of the photosensitive layer is of the second order non-linearity to the exposure amount. With the groove pitch expressed by d, K = 2 .pi./d, the coordinate perpendicular to the groove direction taken as x, and the groove profile .pi.(x) expressed as .pi.(x) = h [sin (Kx) + .gamma.sin (2Kx - 90°)], the parameters h, .gamma. and .PHI. satisfy as follows:
0.26 ? 2h/d ? 0.52 0.05 ? .gamma. ? 0.32.
The wavelength region to be used is normalized by the groove pitch d as 0.67 ? .lambda./d ? 1.1.5. When an incident angle is expressed by .THETA.
and the first order Littrow angle is expressed by .THETA.L, the amount to be used is carried out in such a region that satisfies the following expression:
.THETA.L - 5° ? .THETA. ? .THETA.L + 5°.
A diffraction grating has a reflection film formed on a photosensitive layer disposed on a substrate through exposure followed by development and the groove profile thus formed has a configuration distorted from a sinusoidal form because the sensitivity curve of the photosensitive layer is of the second order non-linearity to the exposure amount. With the groove pitch expressed by d, K = 2 .pi./d, the coordinate perpendicular to the groove direction taken as x, and the groove profile .pi.(x) expressed as .pi.(x) = h [sin (Kx) + .gamma.sin (2Kx - 90°)], the parameters h, .gamma. and .PHI. satisfy as follows:
0.26 ? 2h/d ? 0.52 0.05 ? .gamma. ? 0.32.
The wavelength region to be used is normalized by the groove pitch d as 0.67 ? .lambda./d ? 1.1.5. When an incident angle is expressed by .THETA.
and the first order Littrow angle is expressed by .THETA.L, the amount to be used is carried out in such a region that satisfies the following expression:
.THETA.L - 5° ? .THETA. ? .THETA.L + 5°.
Description
1~2~ ~9~ 61954-14 TITLE OF THE INVENTION
Diffractlon gratlng and manufacturlng method t:hereof.
~AC~GROUND OF THE INVE~TION
1. Field of the Inventlon This inventlon relates to a dif~ractlon gratlng ~or us~
in a spectroscoplc lnstrument, optlcal communication instrument or the llke and a method of manufacturing the same.
Diffractlon gratlng and manufacturlng method t:hereof.
~AC~GROUND OF THE INVE~TION
1. Field of the Inventlon This inventlon relates to a dif~ractlon gratlng ~or us~
in a spectroscoplc lnstrument, optlcal communication instrument or the llke and a method of manufacturing the same.
2. Descrlptlon of the Prlor Art Dlffraction gratlngs have been mainly USQd in optical measuring instrument as a wavelength dlspersion element for selectlvely extracting a preferable wavelength from a certain waveform reglon. However, ln general, the diffraction grating has a dlffractlon efficiency, whlch is largely affected by the wavelength, lncidenk angle and polarization of the incident lighk.
However, if condltions of use are llmited, lt is posslble to optlmlze the sectlonal profile of the gratlng to obtain a high performance dlffraction gratlng. At present, research is being conducted in this area.
For example, an artlcle in Appl. Phys. 24, No. 2 pp.
147-150 ~1981) shows an e~perimental verlficatlon in the microwave region, of the ldea that based on the fact that the manufacture of Fourlor gratlngs by compoælng thelr groove proflle is possible by comblning a fundamental harmonlc and the second order harmonic through holographic exposure technology, the efflciency of Fourlor gratings can be made higher than that of Echelette gratings for wlde wavelength reglon appllcatlons by locally optlmlzln~ the groove proflle of the gratlng theoretlcally, ln the mlcrowav~
' . ;, .
, . . : :
region. ~ 3 2~
Here, the Fourior gratings generally have a groove d profile ~ (x) which can be expressed, with the direction perpendicular to the groove dlrectlon taken as the x-axls and the groove pltch expre~sed as d, ln terms of the i-undamentsl harmonlc K and the second order harmonlc 2K, where K = 2 n~d, as follows:
~ (X) a h [sln (Kx) + ~ sln (2Kx ~ ~)]
where h, ~ and ~ are parameters for determlnlng the proflle. In addltlon, the groove proflle oE dlffractlon gratings describ2d in the above-mentloned article corresponds to the case when h -- 0.42, Y ~ 0.285 and ~ a _900 In the article mentloned ahove, however, the local optlmlzatlon ls mad~ under the condltlon that the angular deviatlon between the llght lncldent to the diffraction grating and the first order dlffracted llght reflected therefrom ls 17.
Thls means that, for example, llght is lncldent thereto at ~ d = 1 rom an angle dlfferent by 8.5 from the Llttrow angle.
When dlffraction gratlngs are employed for optical communlcation appllcatlons, these are used ln the nelghbourhood of the Llttrow mount ln many cases, and there is no case in which these are u~ed whlle malntalnlng an angular devlation of 17.
Therefore, the superiorlty of the Fourior gratings in the local optimization for the Littrow mount is not described ~uantltatively in the above-mentloned artlcle. Thls ls the first problem to be pointed out. Also, although a theoretlcal predlctlon has been verified experlrnentally ln the mlcrowave reglon, the groove profile of dlffractlon gratings actually experlmented with is ~ ;,.
'' ., , ~ 9~ 61954 1~
conslclerably different from that whlch is locally optimlzed.
In general, optical communlcation uses light havlng a wavelength region which ranyes from 0.8~m to :L.55~m which is considerably shorter than that of the rnicrowave region. As a result, it cannot be concluded that the superiorlty of a dlffraction grating locally optlml~ed could be verified Eor all wavelength regions by having it verified only in the mlcrowave region. Thls is the second problern to be polnted out.
In addition, the groove profile ohtalned by the calculation in the above-mentioned article is only appropr:Late for a perfectly conductive groove surface. Therefore, the theoretically calculated proflle ls not valld or a groove sur~ace which is an imperfect conductor.
As to polarization, an article in J. Opt. Soc. Am. A, 3, No. 11 pp. 1780-1787 (1986) describes that lf the light waves polarized perpendlcular and parallel to the groove dlrection are indicated as a TM wave and a TE wave, respectively, the groove profile .ls rectangularr but due to the conductiviky that a metal of the surface of the diffraction yrating has, varlatlon of the efficiency of the TM wave due to the incident angle of a light ls more rapid than that of the TE wave particularly in a wavelength region of several micro or less meters as compared to the situatlon where the reflecting surface is perfectly conductive.
This ls the third problem to be pointed out.
The conventlonal manufacturing method used 18 the two-beam lnterference exposure method uslng a coherent llght, but the photosensitive characterlstlc of a photosensitive layer to be ~ ' ' : ~ .' , ~ 3 ~ 61954-14 t formed on a substrate ls produced in the range ln whlch the film thlckness resldue of the photosensitive layer after development is approximately linearly related wlth the exposure amount, so that in actually maklng Fourior gratings, for example, as seen in Optica Acta 26, No. 11, pp. 1427-1441 (1979), two exposure processes and preclslon posltioning control are required.
In additlon, in the holographlc exposure technology, lt is the general practlce to expose an lnterference pattern obtained by superimposlng plane waves with respect to each other. In thls case, however, slnce the coherent light from a spacial fllter ls a divergent wave, the spaclal coherence will be dlsturbed by optical elements such as, for example, lenses and mlrrors whlch are lnserte~ly disposed between the substrate and the spac:Lal filter ln order to change a ~lveryent wave lnto a plane wave, which causes a sllght distortlon of the lnterference pattern to be exposed. To avoid such a problem, a compllcated optlcal systam is required.
SUMMARY OF THE INVENTION
~n ob~ect of thls lnvention ls to provide a dlffraction grating which has a high dlffraction efficiency in the Llttrow mount and small dependency of the dl~fraction efflclency on the polarlzatlon directlon, and a method of manufacturing the same using a slmple manufacturing system.
In order to attain the above-mentloned ob~ect, a dlffraction grating of thls inventlon comprises, a substrate, a photosensltl~e layer formed on the substrate; and a reflectlon fllm formed on the photosensltlve layer, ln which, where the i~
, - ,.
.
, .~ .:
.
' ~ 3~ 6l95~-l4 dlrection perpendlcular to the groove direction i5 indicatecl by the x-axls, the groove pitch is indicated by d, K = 2 ~d, the groove profile ~x) is glven by:
n(X) = h lsin (Kx) ~ ~ sin (2Kx - 90)]
The parameters h and r satlsfy the followlng condltions:
0 05 _ y c 0.32 0.26 _ 2h/d - 0.52.
The wavelength ~ ls normallzed wlth respect to the groove pltch d, and the normallzed wavelength ~ /cl ls chosen so as to satlsfy the ~ollowlng condition:
0~67 _ ~/d s 1.15.
When the lncldent angle to the fliffraction gratlng and the flrst order Llttrow angle are expressed by ~ and ~L, respectively, the following conclition can be satisfied:
3L - 5 c ~ _ 9L + 5 Wlth the above-described structure, diffractlon efficiency for non-polarlzed llght ls at a level of 85% or more, so that the devlation o~ the diffraction efflclency caused by the polarization of lncldent light does not exceed 10~.
Preferably, y , 2h/cl and ~/d satisfy the following conditlons, 0.1 _ y _ 0.~5 0.35 _ 2h/d _ 0.45 0.70 c ~/d _ 1.1 For manufacturlng the dlffraction grating, a photosensltlve layer formed on a substrate is sub~ect to lnterference exposure followed by clevelopment. The photosensltive , ~ ~
~ :: . , ~
~ 195~-14 layer has a characteri~tlc represented by a characterlstlc curve of the exposure amount versus the film thickness resl~ue of the photosensltlve layer after development. The characteristic curve has a region ln whlch the value of the second order dl~ferentlal of the curve ls posltlve an~ the curve has no third order lnflectlon point. When the exposure intensity distributlon is glven by I(x), and the second and flrst coefficlents of the photosensitive curve ln the region to be exposed obtained by approximating it to a quadratic curve are respectlvely expressed by a and b, the followlng relations can be satisfied, with the exposure intensity distrlbution ~(x) e~pressed as I(x) = Io ~ I
sin (Rx): I
2h/d = Il ¦ b + 2aI0 ¦
and ~ - aIl / 2 ¦ b + ~aIol Preferably, for example, in using a posltlve type photoresist, the followlng relation can be satlsfled Io ~ b / 2a ¦.
In uslng a negative type one, the followlng can be 0 sat lsf led:
b / 2a ¦
whereln b ~ O.
In addltion, in uslng the two-beam lnterference exposure method, a system for producing a dlffraction grating of this inventlon comprlses an exposlng laser, a half-mirror for divldlng llght from an exposlng laser into two ~eams, two sets of mlrrors for reflecting the beam of each of two beams thereby to cause ~32~ 6195~
them to interfere on a photosensitive layer, and two sets of spac.ial filters each comprising a pinhole and a lens for improving the spaclal coherence of the laser beams reElected from the mirrors and for making the beam thus reflected therefrom a divergent wave. When the distance between the pinholes of the spacial filters, the distance between the middle point of the space between the pinholes and the substance to be exposed, and the diameter of -the length of longer side of the substrate to be exposed are expressed by C, H and L, respectively, the following relation is satisfied:
H x C/L2 ~ 32, and ye-t the deviation between the highest and lowest values of the intensity that the envelope o:E exposure intensity distribution on the substrate to be exposed indicates is kept within 20~.
Therefore, in summary, one exemplary aspect o:E the invention provides a diffraction grating for diffracting light incident thereupon, comprising: a substrate; a photosensitive layer formed on said substrate and having formed on a surface thereof a pattern of cyclic grooves; and a reflec-tion film formed on said surface oE said photosensitive layer, wherein said grating has a groove profi.le ~(x) given by:
~ (x) = h[sin(Kx) -~ ~sin(2Kx - 90 )], where a direction perpendicular to the groove is indicated by x-axisr a groove pitch is indicted by d, K = 2rr/d, and parameters h and ~ satisfy the -following conditions:
0.26 ~ 2h/d < 0.52 0.05 < ~ ~ 0032, :
~32~
6195~
wherein when the wavelength ~ of the incident light is normalized with respect to the groove pitch d to a normalized wavelength ~/d, the normalized wavelength ~/d satisies the following condition:
0.67 ~ ~/d Cl-15, and wherein said grating is used in a mount sa-tisfying the following conditiono ~ L ~ 5 ~ ~ < ~L ~ 5 ~
where ~ denotes the incident angle of the incident light and ~L
denotes the first order Li-ttrow angle.
According to another exemplary aspect, there is provided an apparatus for manu:Eacturing a diffraction grating, comprising:
a laser for producing a light; a half mirror Eor dividing the light from said laser into two beams; two mirrors ~or respectively reflecting the two beams in directions toward a photosensitive layer formed on a substrate which has a diameter of longitudinal length L; and two spacial filters each including a pinhole for respectively improving the spacial coherences of the reflected two beams from said two mirrors and for converting the reflected -two beams to two divergent beams of light so that said photosensitive layer is interferentially exposed by the two divergent beams of light, said two spacial filters being spaced ~rom each other by a distance C, and a middle point between the pinholes of said two spacial filters being spaced from said substrate by a distance H, wherein L, C and H satisfy the following condition:
H x C/L2 ~ 32, 7a . .
. .. ~ . .
132~ ~g5 and wherein a deviation of the exposure inten.sity indicated by an envelope oE an exposure intensity distribution on said substrate is within 20%.
BRIEF DESCRIPTION OF THE DRAWINGS
Fig~ 1 is a cross-sectional view of a diEfraction grating of -this invention;
Fig. 2 is a perspective view of the diffrac-tion grating shown in Fig. l;
Fig. 3 is a photosensitive curve of a positive type photosensitive layer and a schematic drawing showing the groove profile of a diEfraction grating formed thereby;
Fig~ 4 is a graph oE the diffraction efEiciency versus the value of 2h/d in the Littrow mount calculated when ~= 0.05, and ~/d = 0.7;
Fig. 5 shows a groove profile when ~= 0.05, and 2h/d = 0.383;
7b ::; , :: ..:- . ...
, ~. ,, ,: .
~L3%1~
6~95~-14 Fig. 6 ls a graph oE the dlffraction efflclency versus the value of 2h/d in the Littrow Mount calculated when r= 0.32 and ~/d ~ 0.9;
Fig. 7 shows the groove proflle when Y~ 0.32 and 2h~d = 0.40i Flg. 8 is a graph of the diffractlon eEflclency versus the value of 2h/d in the Llttrow mount calculated when ~ 0.1 and ~d = 0.67;
Flg. 9 shows the groove profile when r = 0~1 and 2hJd = 0.35;
Fig. 10 is a graph of the dlffraction efficlency versus the value of 2h/d ln the Littrow mount calculated when Y ~ 0.2 and ~/d = 0.8;
Fig. 11 is a graph of the difEraction efficlency versus the value of ~ /d in the Llttrow mount calculated when Y = 0.2 and 2h/d = 0.47;
Fig. 12 shows the groove proflle when r = 0.2 and 2h/d = 0.47;
Fig. I3 is a graph of the diffraction efficiency versus the value of ~/d in the Littrow mount calculated when Y = 0.2 and 2h/d = 0.435~
Fig. 14. is a graph of the dependence of the diffraction efficiency of a diffraction gratlng measured under the conditions r= 0.2, ~/d = 1.0 and 2h/d - 0.435 of the incident angle of a light;
Fig. 15 is a scanning electron microscopic ~SEM) observation of the dlffraction gratlng to be measured;
132~9~
Fig. 16 ls a schematic dlagram lllustrating an emkodiment of a manufacturing method of the diffraction grating shown in Fig. l; and Fig. 17 ls a graph showing the range that the d~viatlon of the spacing of lnterference patterns exposed on the surface of a substrate ls wikhin 1~.
DESCRIPTION OF THE PR~F~RRED EMBODIMENTS
In F'ig. 1, the reference numerals l:L, 12 and 13 designate a substrate, a photosensltive layer and a reflection film, respectlvely.
On the substrate 11 ls disposed the photosensitive layer 12 in whlch cyclic grooves are patterned using a holograph:Lc exposure. Then, the reflection film 13 is ~ormed thereon havlng a thlnness to a degree such that the groove profile patterned in the photosensltlve layer 12 is not damaged, thereby to construct a diffraction gratlng.
Fig. 2 1s a perspectlve view of the diffraction grating shown in Fig. 1. The re~erence numerals 21, 22 and 23 lndicate a substrate, a photosensltive layer and a reflection film, respectively. The substrate shown in thls ~igure is plane and rectangular, but the shape thereof is not limited to this.
Intenslty distributlon of a light to be directed onto photosensitive layer through the holographic technology is generally expressed ln a trigonometrically functional form in case of the two-beam interference exposure of a coherent llght. If this is directly transferred to the photosensitive layer, it wlll becorne a slnusoidal form, so that by ylving a nonllnearlty to the .
. , - : ~ . -,:,. :
:: . . :, , 1321~9~
photosensltive characterlstic of the photosensitive layer, the groove proflle after development can be made so that lt wlll be distorte~ from the sinusoldal form.
In Fig. 3, the reference numerals 31, 32 and 33 indicate an intensity distribution of an expoæure llght, a photosensltlve curve of a positive type photosensitlve layer, i.e., a photosensitlve layer the exposed area of which is removed after development, and a groove profile obtained after development, respectively. This figure show~ one embodiment for maklng such condltions as y = 0.2 and 2h/d ~ 0.435 realizable ln Fourior gratings, in which, with the intensity distrlbution of a light to be exposed expressed as I(x) = Io + Il sin (Kx), the following conditions are obtained:
Io - 2.32 mJ, Il = 1.74 mJ and d = 0.348 ~m.
In addition, with the curve obtained by approximating the photosensitlve curve showing the film thickness resldue Q /Qo ln the exposed area of the photosensitlve layer to a quadratic Eunctlon expressed as R/l~O = aI2 ~ bI + c, the followlng condltions are obtalned:
a ~ 0.1, b r -0~899 and c = 0.25.
If the area of the photosensitive layer to be exposed can be approximated to a quadratic curve, then there exists no inflection point of the third order. The lntensity distribution 31 of an lnterference llght is expressed in tha trlgonometrically functional form and the photosensltive curve 32 has a . . : - . . ~ : :
,. . .. .
~32~9~
characterlstic such that the second order dlfferential coefflcient ls always posltlve ln the area to be exposed, As a result, the change in the film thlckness resldue of the photosensltlve layer ln the area to be exposed ls decreased wlth an increase ln exposure amount. Thus, lf the exposure ls carried out under the condition of the intenslty distrlbution 31, then the groove proflle 33 after development wlll have a profile which ls distorted from a slnusoidal form in that the top portion of the groove is narrowed and the root portion thereof is made round.
And a diffraction grating can be constructed by forming a thin reflection film whlch has such a deyree of thinness that it will not damage the groove profile on the photosensitlve layer~ The above-described emhodiment has a positive type photoresist, but it is easily understood that lf a negatlve type one, i.e., a photoresist in which the unexposed area of a photosensltive lay~r is removed after development, is used; the same result is obtainable. Thus, the above-exemplifled numerlcal values are not llmited to them.
In Flg. ~, condltlons such as r = 0,05 and ~/d ~ 0.7 are used. A curve 41 shown by the contlnuous line lndicates the dlffraction efficiency Eor the TE wave, and a curve 42 shown by the alternate long and short dash llne indicates the dlffraction efflclency for the TM wave. A curve 43 shown by the short dashes line lndicates the di~raction efficiency obtained when an incident light is non-polarized, The diffraction grating is constructed through numerical procedures described in J. Opt. Soc.
Arn. A 4, pp. 465-472 (1987~ under the Littrow mount condition and ,~ 11 . ~, ' ~ ' . . ' !
, ` , ,. ` '. . ` ~ ' ` ~ . : , ' . ' " '. `' : ' " ' '. .
~2~
the surface thereof is made perfectly conductive. The reglon ln whlch the diffractlon efficlency 43 when the lncldent llght ls non-polarlzed exceeds 85% ls as follows:
0.26 ~ 2h/d ~ 0.46.
As to the deviatlon of the diffraction efflciency due to the polarlzation, partlcularly when 0.26 _ 2h/d .< 0.44, lt ls kept wlthin 10%, which means that the dependence of dlffraction efflclency on polarl7atlon ls small Flg. 5 shows the groove profile of the dlffraction gratlng for which the numerlcal calculatlons were carrled out.
Thls is slightly distorted from the slnusoldal groove profile by an arnount at whlch the second order harmonlc is added.
In Flg. 6, condltions such as y= 0.32 and ~d = 0.9 are used. The region ln which a diffraction efflciency 63 for non-polarlzed llght exceeds 85% is as follows:
0.31 s 2h/d _0.46.
In this reglon, the deviation of the dif~raction efficiency due to the polarizatlon is kept wi~hin 8%.
Flg. 7 shows the groove proflle of the dlfractlon gratlng for which the numerlcal calculatlons were carrled out. As the dlstortlon from the slnusoidal form ls lncreased, the region in whlch the dlffractlon efficlency is hlgh ls shlfted ln the directlon that the value of 2h/d ls increased.
Fig. 8 shows the case that condltions such as y = 0.1 and ~/d = 0.67 are used. The reglon in whlch a dl~fraction efflclency 83 for non-polarlzed llght e~ceeds ~5% is as follows:
~: . ,, , : :
. , .
~ . , - . : . : , .
., 1 3 2 ~ j 6~954 l4 0.26 s 2h/d s 0,43.
In thls reg.ton, the devlatlon of the diffractlon efflclency due to the polarlzation is kept with~n 5%, which means that lts dependence on polarlæatlon is par~icularly small. Flg. 9 shows the groove profile of the diffractlon grating for whlch the numerical calculatlons were carried out.
Fig. 10 shows t~e case that con~itions such as ~ = 0.2 and ~d = 0.8 are used. The reglon in whlch a dlffraction efficiency lOc for non-polarlzed light exceeds 85~ ls as follows:
0.29 s 2h/d 5 0.48.
This mPans that a considerably wide reglon of 2h/d is malntained.
In this region, the ~eviatlon of the dlffraction efficiency due to the polarization ls kept within 10%.
Fig. 11 is a graph showing the dependence of diffractlon efflciency on wavelength when 2h/d = 0.47 is taken in Flg. 10.
The region in which a diffraction efficiency llc for non-polarized li~ht exceeds 85% is as follows, 0.78 c ~/d c 1.15.
However, in the reglon of 0.88 ~ ~/d ~ 1.0, the deviations oE
diffractlon e~ficlencles for light of both polarlzatlons become large. Fig. 12 shows the groove profile of the dlffraction grating for which the numerical calculakions were carried out.
Fig. 13 ls a graph showing the dependence of dlffraction efficiency on wavelength when 2h/d ~ 0.435 where the dlffraction efflclencles for light of both polariæations are equal to each other in Fig. 10 is taken. The region in whlch a dlffractiQn efficiency 13c for non-polarlzed light exceeds 85% ls as follows:
' ~~
- . , . ,, : ~
~ 3 2 ~ 61954-1~
0.70 _ ~d < 1.15.
Partlcu].arly, ln a wide region of wavelengths satlsfying such a conditlon as 0.73 < ~/d _1.07, the deviation of the dlffractlon efficlency due to the polariæatlon 15 kept wlthin 10~.
Fig. 14 shows ~he dependence of dlffraction efflciency on lncident angle resultlng from measurements uslng a diffraction gratlng actually produced by formlng a photosensltlve layer on a glass substrate and then applylng the holographlc e~posure thereto. The groove pltch ~dlstance between ad~acent two grooves) is 1.3 ym, and on the surface thereof is evaporated gold whose reflectlvity exceeds 99~, and a semiconductor laser of a 1.3 ~m band was used as a test light.
In Flg. 14, an lncident angle of 30 corresponds to the Littrow angle. The curve 14a ls Eor the dlffractlon efficlency of the TE wave, the curve 14b for the diffraction efficiency of the TM wave, and the curve 14c for that of non-polarized light. Marks ~ and ~ show polnts measured for the TE wave 14a and the TM
wave 14b, respectlvely. Generally, under such a condltlon as ~/d ~ 1, the dlffraction efflciency is increased in the flrst order Llttrow mount, and lt is decreased as the incident angle moves farther apart frorn the Llttrow anyle. As seen in Fig. 14, for light of both polarizatlons, the maxlmum value of diffractlon efficlency is obtained at the Llttrow mount and a diffractlon efEiciency as hlgh as 95~ is obtalned for non-polarlzed light.
The diffraction efflclencles at that tlme are approximately identical to calculated values in Fig. 13. As is clear from Fig.
14, the diffraction eEficiency for an incldent angle ln a range of , . , , , "
, . :
~2~9~ 61~5~-~4 5~ from the Llttrow angle rnalntalns 85~ or more for non-polarlzed llght, and the efficiency deviat:lon due to polarization is suf~iciently small to be within 10~. In case that an lncident angle is 5 from the Littrow angle, the angular deviation between the incident angle and the reflection angle of the flrst order diffracted llght corresponds to 10~.
Further as clear ~rom Fig. 14, if a light ls incident from an angle greater than thls, the diffractlon efflciency 14b of the TM wave ls rapldly decreased due to the permittlvity of the surface of dlffraction grating as compared wlth the dlffractlon efficlency 14a of the TE wave. For example, when a llght ls incldent from an angle 10~ Erom the Littrow angle, the deviation of dlffractlon efflclency between both polarizations exceeds 20%, so that the diffraction efflclency 14c for non-polarlzed llght wl 1 1 becorne low.
In Flg. 15, the groove profile of the dlffractlon gratlng used for measurement ls observed by using SEM (Scanning Electron Mlcroscopy). In this case, the groove proflle has a proflle corresponding to condltlons ~uch as r = 0.2, ~/d ~ 1.0 and 2h/d = 0.435. In addltlon, various proflles can be provlded by changlng the comblnatlon of parameters 2h/d, y and ~d. As a result, the inventlon is not llmited to the above-mentloned embodlments.
In Flg. 16, an exposing laser ls indicated at 16a, mirrors are indlcated at 16b, 16c and 16d, a beam s~lltter at 16e, spaclal filters consisting of a lens and pinhole at 16~ and 16g, a photosensitlve layer at 16h and a substrate at 161. The mlrrors , :-:
. .
: - , ~ 3 ~ 195~-14 16c and 16d are dlsposed so that the beams divided into two wlll lnterfere wlth each other on the photosensltlve layer 16h of the substrate 16i.
A coherent llght sent from the exposing laser 16a is reflected by the mlrror 16b and then divld2d lnto two beams through the beam splltter 16e. The beams thus divided are respectively reflected by the mlrrors 16c and 16d to go to the spaclal fllters 16f and 16g thereby to lncrease thelr spacial coherence and to become divergent waves, thus being superimposed to each other on the photosensltlve layer 16h. It ls described, for example, ln E. Wolf, "Progress ln Optlcs XIV", ch. V, pp. 205 (North-Holland 1976) that an lnterference pattern produced by superlmposlng divergent waves on each other generally ls ln the hyperbollc form.
Referrin~ to Fig. 17, when the distance between the pinholes of the spaclal fllters 16f and 16g ls expressed by C, the distance between the middle polnt of the space between the pinholes and the photosensitive layer 16h ls e~pressed by H, and the length of longer side of the substrate 16i ls expressed ~y L, lt ls shown that the rate of the difference of the pattern interval between the interference patterns at the edge portlon of the substrate 161 (dl) and the pattern interval between tho~e at the center portlon thereof (dO), i.e., (dl - dO) /dO, does not exceed 1%. In Flg. 17, the ordinate and abscissa are C/L and H/L, respectlvely. A boundary line 17a lndicates a curve where the ratlo of dlfference becomes 1%, and the shaded area indi.cates the re~ion where lt ls below 1~. The boundary llne 17a satlsfies t'he . ~ ,.
: -. ' followlng condltion: ~ ~ 2 C x H/L2 = 32 As a result, the lnterference pattern to be exposed under the conditlon of C 2 H/L _ 32 can have the pattern interval kept within 1% on the surface of a substrate to be exposed by adopting only a part of the interference patterns of the hyperbollc form as shown ln Fig. 16, so that the interference pattern can be regarded to be llnear. Therefore, there is no need to use any optlcal lnstrument between the spacial fllters and substrate. Thls means that the spaclal coherence is lmproved and interference expo~ure can he achieved by uslng an optical system which is simple ln structure.
In additl~n, slnce the envelope of the lntenslty distributlon on the photosensitive layer 16h is of the Gaussian distrlbutlon, in order to obtain a uniform groove profile all over the substrate in performlng the exposure for a constant period of time, lt ls required that the devlation of the intensity of the envelope o a llght to be exposed all over the substrate be kept wlthin 20% at the central portion where it ls hl~hest and the edge portion where lt ls lowest. For example, when the deviation of exposure lntenslty of an actually produced diffraction grantlng ls 20~, even when non-polarized, a diffractlon efficiency of 80~ or more can be obtained.
As an example of such structure, when settings such as L = 30 mm, H - 600 mm and C = 400 mm are used, and an ob~ective lens with a magniflcatlon of 40 ls used ln the spaclal filter, the dlameter of a beam to be lnterfered on the substrate ls 140 mm, , , . -. .
. :, .
.. ~, . . .
,, :: , :
~32~
the devlation in the envelope of lntenslty distribution on the surface of the photosensitive layer to be exposed ls kept wlthin 10%, the value of C x H~L2 is 260, and the deviation between the interval of the interference patterns at the central and edge portlons of the substrate is kept within 0.1~, which means that no problem arlses practically.
Also, the mirror 16b shown in Fig. 16 can be omltted.
No limitation is ma~e to the above-descrlbed embodlments.
"
. ~ .
... . . : -~
However, if condltions of use are llmited, lt is posslble to optlmlze the sectlonal profile of the gratlng to obtain a high performance dlffraction gratlng. At present, research is being conducted in this area.
For example, an artlcle in Appl. Phys. 24, No. 2 pp.
147-150 ~1981) shows an e~perimental verlficatlon in the microwave region, of the ldea that based on the fact that the manufacture of Fourlor gratlngs by compoælng thelr groove proflle is possible by comblning a fundamental harmonlc and the second order harmonic through holographic exposure technology, the efflciency of Fourlor gratings can be made higher than that of Echelette gratings for wlde wavelength reglon appllcatlons by locally optlmlzln~ the groove proflle of the gratlng theoretlcally, ln the mlcrowav~
' . ;, .
, . . : :
region. ~ 3 2~
Here, the Fourior gratings generally have a groove d profile ~ (x) which can be expressed, with the direction perpendicular to the groove dlrectlon taken as the x-axls and the groove pltch expre~sed as d, ln terms of the i-undamentsl harmonlc K and the second order harmonlc 2K, where K = 2 n~d, as follows:
~ (X) a h [sln (Kx) + ~ sln (2Kx ~ ~)]
where h, ~ and ~ are parameters for determlnlng the proflle. In addltlon, the groove proflle oE dlffractlon gratings describ2d in the above-mentloned article corresponds to the case when h -- 0.42, Y ~ 0.285 and ~ a _900 In the article mentloned ahove, however, the local optlmlzatlon ls mad~ under the condltlon that the angular deviatlon between the llght lncldent to the diffraction grating and the first order dlffracted llght reflected therefrom ls 17.
Thls means that, for example, llght is lncldent thereto at ~ d = 1 rom an angle dlfferent by 8.5 from the Llttrow angle.
When dlffraction gratlngs are employed for optical communlcation appllcatlons, these are used ln the nelghbourhood of the Llttrow mount ln many cases, and there is no case in which these are u~ed whlle malntalnlng an angular devlation of 17.
Therefore, the superiorlty of the Fourior gratings in the local optimization for the Littrow mount is not described ~uantltatively in the above-mentloned artlcle. Thls ls the first problem to be pointed out. Also, although a theoretlcal predlctlon has been verified experlrnentally ln the mlcrowave reglon, the groove profile of dlffractlon gratings actually experlmented with is ~ ;,.
'' ., , ~ 9~ 61954 1~
conslclerably different from that whlch is locally optimlzed.
In general, optical communlcation uses light havlng a wavelength region which ranyes from 0.8~m to :L.55~m which is considerably shorter than that of the rnicrowave region. As a result, it cannot be concluded that the superiorlty of a dlffraction grating locally optlml~ed could be verified Eor all wavelength regions by having it verified only in the mlcrowave region. Thls is the second problern to be polnted out.
In addition, the groove profile ohtalned by the calculation in the above-mentioned article is only appropr:Late for a perfectly conductive groove surface. Therefore, the theoretically calculated proflle ls not valld or a groove sur~ace which is an imperfect conductor.
As to polarization, an article in J. Opt. Soc. Am. A, 3, No. 11 pp. 1780-1787 (1986) describes that lf the light waves polarized perpendlcular and parallel to the groove dlrection are indicated as a TM wave and a TE wave, respectively, the groove profile .ls rectangularr but due to the conductiviky that a metal of the surface of the diffraction yrating has, varlatlon of the efficiency of the TM wave due to the incident angle of a light ls more rapid than that of the TE wave particularly in a wavelength region of several micro or less meters as compared to the situatlon where the reflecting surface is perfectly conductive.
This ls the third problem to be pointed out.
The conventlonal manufacturing method used 18 the two-beam lnterference exposure method uslng a coherent llght, but the photosensitive characterlstlc of a photosensitive layer to be ~ ' ' : ~ .' , ~ 3 ~ 61954-14 t formed on a substrate ls produced in the range ln whlch the film thlckness resldue of the photosensitive layer after development is approximately linearly related wlth the exposure amount, so that in actually maklng Fourior gratings, for example, as seen in Optica Acta 26, No. 11, pp. 1427-1441 (1979), two exposure processes and preclslon posltioning control are required.
In additlon, in the holographlc exposure technology, lt is the general practlce to expose an lnterference pattern obtained by superimposlng plane waves with respect to each other. In thls case, however, slnce the coherent light from a spacial fllter ls a divergent wave, the spaclal coherence will be dlsturbed by optical elements such as, for example, lenses and mlrrors whlch are lnserte~ly disposed between the substrate and the spac:Lal filter ln order to change a ~lveryent wave lnto a plane wave, which causes a sllght distortlon of the lnterference pattern to be exposed. To avoid such a problem, a compllcated optlcal systam is required.
SUMMARY OF THE INVENTION
~n ob~ect of thls lnvention ls to provide a dlffraction grating which has a high dlffraction efficiency in the Llttrow mount and small dependency of the dl~fraction efflclency on the polarlzatlon directlon, and a method of manufacturing the same using a slmple manufacturing system.
In order to attain the above-mentloned ob~ect, a dlffraction grating of thls inventlon comprises, a substrate, a photosensltl~e layer formed on the substrate; and a reflectlon fllm formed on the photosensltlve layer, ln which, where the i~
, - ,.
.
, .~ .:
.
' ~ 3~ 6l95~-l4 dlrection perpendlcular to the groove direction i5 indicatecl by the x-axls, the groove pitch is indicated by d, K = 2 ~d, the groove profile ~x) is glven by:
n(X) = h lsin (Kx) ~ ~ sin (2Kx - 90)]
The parameters h and r satlsfy the followlng condltions:
0 05 _ y c 0.32 0.26 _ 2h/d - 0.52.
The wavelength ~ ls normallzed wlth respect to the groove pltch d, and the normallzed wavelength ~ /cl ls chosen so as to satlsfy the ~ollowlng condition:
0~67 _ ~/d s 1.15.
When the lncldent angle to the fliffraction gratlng and the flrst order Llttrow angle are expressed by ~ and ~L, respectively, the following conclition can be satisfied:
3L - 5 c ~ _ 9L + 5 Wlth the above-described structure, diffractlon efficiency for non-polarlzed llght ls at a level of 85% or more, so that the devlation o~ the diffraction efflclency caused by the polarization of lncldent light does not exceed 10~.
Preferably, y , 2h/cl and ~/d satisfy the following conditlons, 0.1 _ y _ 0.~5 0.35 _ 2h/d _ 0.45 0.70 c ~/d _ 1.1 For manufacturlng the dlffraction grating, a photosensltlve layer formed on a substrate is sub~ect to lnterference exposure followed by clevelopment. The photosensltive , ~ ~
~ :: . , ~
~ 195~-14 layer has a characteri~tlc represented by a characterlstlc curve of the exposure amount versus the film thickness resl~ue of the photosensltlve layer after development. The characteristic curve has a region ln whlch the value of the second order dl~ferentlal of the curve ls posltlve an~ the curve has no third order lnflectlon point. When the exposure intensity distributlon is glven by I(x), and the second and flrst coefficlents of the photosensitive curve ln the region to be exposed obtained by approximating it to a quadratic curve are respectlvely expressed by a and b, the followlng relations can be satisfied, with the exposure intensity distrlbution ~(x) e~pressed as I(x) = Io ~ I
sin (Rx): I
2h/d = Il ¦ b + 2aI0 ¦
and ~ - aIl / 2 ¦ b + ~aIol Preferably, for example, in using a posltlve type photoresist, the followlng relation can be satlsfled Io ~ b / 2a ¦.
In uslng a negative type one, the followlng can be 0 sat lsf led:
b / 2a ¦
whereln b ~ O.
In addltion, in uslng the two-beam lnterference exposure method, a system for producing a dlffraction grating of this inventlon comprlses an exposlng laser, a half-mirror for divldlng llght from an exposlng laser into two ~eams, two sets of mlrrors for reflecting the beam of each of two beams thereby to cause ~32~ 6195~
them to interfere on a photosensitive layer, and two sets of spac.ial filters each comprising a pinhole and a lens for improving the spaclal coherence of the laser beams reElected from the mirrors and for making the beam thus reflected therefrom a divergent wave. When the distance between the pinholes of the spacial filters, the distance between the middle point of the space between the pinholes and the substance to be exposed, and the diameter of -the length of longer side of the substrate to be exposed are expressed by C, H and L, respectively, the following relation is satisfied:
H x C/L2 ~ 32, and ye-t the deviation between the highest and lowest values of the intensity that the envelope o:E exposure intensity distribution on the substrate to be exposed indicates is kept within 20~.
Therefore, in summary, one exemplary aspect o:E the invention provides a diffraction grating for diffracting light incident thereupon, comprising: a substrate; a photosensitive layer formed on said substrate and having formed on a surface thereof a pattern of cyclic grooves; and a reflec-tion film formed on said surface oE said photosensitive layer, wherein said grating has a groove profi.le ~(x) given by:
~ (x) = h[sin(Kx) -~ ~sin(2Kx - 90 )], where a direction perpendicular to the groove is indicated by x-axisr a groove pitch is indicted by d, K = 2rr/d, and parameters h and ~ satisfy the -following conditions:
0.26 ~ 2h/d < 0.52 0.05 < ~ ~ 0032, :
~32~
6195~
wherein when the wavelength ~ of the incident light is normalized with respect to the groove pitch d to a normalized wavelength ~/d, the normalized wavelength ~/d satisies the following condition:
0.67 ~ ~/d Cl-15, and wherein said grating is used in a mount sa-tisfying the following conditiono ~ L ~ 5 ~ ~ < ~L ~ 5 ~
where ~ denotes the incident angle of the incident light and ~L
denotes the first order Li-ttrow angle.
According to another exemplary aspect, there is provided an apparatus for manu:Eacturing a diffraction grating, comprising:
a laser for producing a light; a half mirror Eor dividing the light from said laser into two beams; two mirrors ~or respectively reflecting the two beams in directions toward a photosensitive layer formed on a substrate which has a diameter of longitudinal length L; and two spacial filters each including a pinhole for respectively improving the spacial coherences of the reflected two beams from said two mirrors and for converting the reflected -two beams to two divergent beams of light so that said photosensitive layer is interferentially exposed by the two divergent beams of light, said two spacial filters being spaced ~rom each other by a distance C, and a middle point between the pinholes of said two spacial filters being spaced from said substrate by a distance H, wherein L, C and H satisfy the following condition:
H x C/L2 ~ 32, 7a . .
. .. ~ . .
132~ ~g5 and wherein a deviation of the exposure inten.sity indicated by an envelope oE an exposure intensity distribution on said substrate is within 20%.
BRIEF DESCRIPTION OF THE DRAWINGS
Fig~ 1 is a cross-sectional view of a diEfraction grating of -this invention;
Fig. 2 is a perspective view of the diffrac-tion grating shown in Fig. l;
Fig. 3 is a photosensitive curve of a positive type photosensitive layer and a schematic drawing showing the groove profile of a diEfraction grating formed thereby;
Fig~ 4 is a graph oE the diffraction efEiciency versus the value of 2h/d in the Littrow mount calculated when ~= 0.05, and ~/d = 0.7;
Fig. 5 shows a groove profile when ~= 0.05, and 2h/d = 0.383;
7b ::; , :: ..:- . ...
, ~. ,, ,: .
~L3%1~
6~95~-14 Fig. 6 ls a graph oE the dlffraction efflclency versus the value of 2h/d in the Littrow Mount calculated when r= 0.32 and ~/d ~ 0.9;
Fig. 7 shows the groove proflle when Y~ 0.32 and 2h~d = 0.40i Flg. 8 is a graph of the diffractlon eEflclency versus the value of 2h/d in the Llttrow mount calculated when ~ 0.1 and ~d = 0.67;
Flg. 9 shows the groove profile when r = 0~1 and 2hJd = 0.35;
Fig. 10 is a graph of the dlffraction efficlency versus the value of 2h/d ln the Littrow mount calculated when Y ~ 0.2 and ~/d = 0.8;
Fig. 11 is a graph of the difEraction efficlency versus the value of ~ /d in the Llttrow mount calculated when Y = 0.2 and 2h/d = 0.47;
Fig. 12 shows the groove proflle when r = 0.2 and 2h/d = 0.47;
Fig. I3 is a graph of the diffraction efficiency versus the value of ~/d in the Littrow mount calculated when Y = 0.2 and 2h/d = 0.435~
Fig. 14. is a graph of the dependence of the diffraction efficiency of a diffraction gratlng measured under the conditions r= 0.2, ~/d = 1.0 and 2h/d - 0.435 of the incident angle of a light;
Fig. 15 is a scanning electron microscopic ~SEM) observation of the dlffraction gratlng to be measured;
132~9~
Fig. 16 ls a schematic dlagram lllustrating an emkodiment of a manufacturing method of the diffraction grating shown in Fig. l; and Fig. 17 ls a graph showing the range that the d~viatlon of the spacing of lnterference patterns exposed on the surface of a substrate ls wikhin 1~.
DESCRIPTION OF THE PR~F~RRED EMBODIMENTS
In F'ig. 1, the reference numerals l:L, 12 and 13 designate a substrate, a photosensltive layer and a reflection film, respectlvely.
On the substrate 11 ls disposed the photosensitive layer 12 in whlch cyclic grooves are patterned using a holograph:Lc exposure. Then, the reflection film 13 is ~ormed thereon havlng a thlnness to a degree such that the groove profile patterned in the photosensltlve layer 12 is not damaged, thereby to construct a diffraction gratlng.
Fig. 2 1s a perspectlve view of the diffraction grating shown in Fig. 1. The re~erence numerals 21, 22 and 23 lndicate a substrate, a photosensltive layer and a reflection film, respectively. The substrate shown in thls ~igure is plane and rectangular, but the shape thereof is not limited to this.
Intenslty distributlon of a light to be directed onto photosensitive layer through the holographic technology is generally expressed ln a trigonometrically functional form in case of the two-beam interference exposure of a coherent llght. If this is directly transferred to the photosensitive layer, it wlll becorne a slnusoidal form, so that by ylving a nonllnearlty to the .
. , - : ~ . -,:,. :
:: . . :, , 1321~9~
photosensltive characterlstic of the photosensitive layer, the groove proflle after development can be made so that lt wlll be distorte~ from the sinusoldal form.
In Fig. 3, the reference numerals 31, 32 and 33 indicate an intensity distribution of an expoæure llght, a photosensltlve curve of a positive type photosensitlve layer, i.e., a photosensitlve layer the exposed area of which is removed after development, and a groove profile obtained after development, respectively. This figure show~ one embodiment for maklng such condltions as y = 0.2 and 2h/d ~ 0.435 realizable ln Fourior gratings, in which, with the intensity distrlbution of a light to be exposed expressed as I(x) = Io + Il sin (Kx), the following conditions are obtained:
Io - 2.32 mJ, Il = 1.74 mJ and d = 0.348 ~m.
In addition, with the curve obtained by approximating the photosensitlve curve showing the film thickness resldue Q /Qo ln the exposed area of the photosensitlve layer to a quadratic Eunctlon expressed as R/l~O = aI2 ~ bI + c, the followlng condltions are obtalned:
a ~ 0.1, b r -0~899 and c = 0.25.
If the area of the photosensitive layer to be exposed can be approximated to a quadratic curve, then there exists no inflection point of the third order. The lntensity distribution 31 of an lnterference llght is expressed in tha trlgonometrically functional form and the photosensltive curve 32 has a . . : - . . ~ : :
,. . .. .
~32~9~
characterlstic such that the second order dlfferential coefflcient ls always posltlve ln the area to be exposed, As a result, the change in the film thlckness resldue of the photosensltlve layer ln the area to be exposed ls decreased wlth an increase ln exposure amount. Thus, lf the exposure ls carried out under the condition of the intenslty distrlbution 31, then the groove proflle 33 after development wlll have a profile which ls distorted from a slnusoidal form in that the top portion of the groove is narrowed and the root portion thereof is made round.
And a diffraction grating can be constructed by forming a thin reflection film whlch has such a deyree of thinness that it will not damage the groove profile on the photosensitlve layer~ The above-described emhodiment has a positive type photoresist, but it is easily understood that lf a negatlve type one, i.e., a photoresist in which the unexposed area of a photosensltive lay~r is removed after development, is used; the same result is obtainable. Thus, the above-exemplifled numerlcal values are not llmited to them.
In Flg. ~, condltlons such as r = 0,05 and ~/d ~ 0.7 are used. A curve 41 shown by the contlnuous line lndicates the dlffraction efficiency Eor the TE wave, and a curve 42 shown by the alternate long and short dash llne indicates the dlffraction efflclency for the TM wave. A curve 43 shown by the short dashes line lndicates the di~raction efficiency obtained when an incident light is non-polarized, The diffraction grating is constructed through numerical procedures described in J. Opt. Soc.
Arn. A 4, pp. 465-472 (1987~ under the Littrow mount condition and ,~ 11 . ~, ' ~ ' . . ' !
, ` , ,. ` '. . ` ~ ' ` ~ . : , ' . ' " '. `' : ' " ' '. .
~2~
the surface thereof is made perfectly conductive. The reglon ln whlch the diffractlon efficlency 43 when the lncldent llght ls non-polarlzed exceeds 85% ls as follows:
0.26 ~ 2h/d ~ 0.46.
As to the deviatlon of the diffraction efflciency due to the polarlzation, partlcularly when 0.26 _ 2h/d .< 0.44, lt ls kept wlthin 10%, which means that the dependence of dlffraction efflclency on polarl7atlon ls small Flg. 5 shows the groove profile of the dlffraction gratlng for which the numerlcal calculatlons were carrled out.
Thls is slightly distorted from the slnusoldal groove profile by an arnount at whlch the second order harmonlc is added.
In Flg. 6, condltions such as y= 0.32 and ~d = 0.9 are used. The region ln which a diffraction efflciency 63 for non-polarlzed llght exceeds 85% is as follows:
0.31 s 2h/d _0.46.
In this reglon, the deviation of the dif~raction efficiency due to the polarizatlon is kept wi~hin 8%.
Flg. 7 shows the groove proflle of the dlfractlon gratlng for which the numerlcal calculatlons were carrled out. As the dlstortlon from the slnusoidal form ls lncreased, the region in whlch the dlffractlon efficlency is hlgh ls shlfted ln the directlon that the value of 2h/d ls increased.
Fig. 8 shows the case that condltions such as y = 0.1 and ~/d = 0.67 are used. The reglon in whlch a dl~fraction efflclency 83 for non-polarlzed llght e~ceeds ~5% is as follows:
~: . ,, , : :
. , .
~ . , - . : . : , .
., 1 3 2 ~ j 6~954 l4 0.26 s 2h/d s 0,43.
In thls reg.ton, the devlatlon of the diffractlon efflclency due to the polarlzation is kept with~n 5%, which means that lts dependence on polarlæatlon is par~icularly small. Flg. 9 shows the groove profile of the diffractlon grating for whlch the numerical calculatlons were carried out.
Fig. 10 shows t~e case that con~itions such as ~ = 0.2 and ~d = 0.8 are used. The reglon in whlch a dlffraction efficiency lOc for non-polarlzed light exceeds 85~ ls as follows:
0.29 s 2h/d 5 0.48.
This mPans that a considerably wide reglon of 2h/d is malntained.
In this region, the ~eviatlon of the dlffraction efficiency due to the polarization ls kept within 10%.
Fig. 11 is a graph showing the dependence of diffractlon efflciency on wavelength when 2h/d = 0.47 is taken in Flg. 10.
The region in which a diffraction efficiency llc for non-polarized li~ht exceeds 85% is as follows, 0.78 c ~/d c 1.15.
However, in the reglon of 0.88 ~ ~/d ~ 1.0, the deviations oE
diffractlon e~ficlencles for light of both polarlzatlons become large. Fig. 12 shows the groove profile of the dlffraction grating for which the numerical calculakions were carried out.
Fig. 13 ls a graph showing the dependence of dlffraction efficiency on wavelength when 2h/d ~ 0.435 where the dlffraction efflclencles for light of both polariæations are equal to each other in Fig. 10 is taken. The region in whlch a dlffractiQn efficiency 13c for non-polarlzed light exceeds 85% ls as follows:
' ~~
- . , . ,, : ~
~ 3 2 ~ 61954-1~
0.70 _ ~d < 1.15.
Partlcu].arly, ln a wide region of wavelengths satlsfying such a conditlon as 0.73 < ~/d _1.07, the deviation of the dlffractlon efficlency due to the polariæatlon 15 kept wlthin 10~.
Fig. 14 shows ~he dependence of dlffraction efflciency on lncident angle resultlng from measurements uslng a diffraction gratlng actually produced by formlng a photosensltlve layer on a glass substrate and then applylng the holographlc e~posure thereto. The groove pltch ~dlstance between ad~acent two grooves) is 1.3 ym, and on the surface thereof is evaporated gold whose reflectlvity exceeds 99~, and a semiconductor laser of a 1.3 ~m band was used as a test light.
In Flg. 14, an lncident angle of 30 corresponds to the Littrow angle. The curve 14a ls Eor the dlffractlon efficlency of the TE wave, the curve 14b for the diffraction efficiency of the TM wave, and the curve 14c for that of non-polarized light. Marks ~ and ~ show polnts measured for the TE wave 14a and the TM
wave 14b, respectlvely. Generally, under such a condltlon as ~/d ~ 1, the dlffraction efflciency is increased in the flrst order Llttrow mount, and lt is decreased as the incident angle moves farther apart frorn the Llttrow anyle. As seen in Fig. 14, for light of both polarizatlons, the maxlmum value of diffractlon efficlency is obtained at the Llttrow mount and a diffractlon efEiciency as hlgh as 95~ is obtalned for non-polarlzed light.
The diffraction efflclencles at that tlme are approximately identical to calculated values in Fig. 13. As is clear from Fig.
14, the diffraction eEficiency for an incldent angle ln a range of , . , , , "
, . :
~2~9~ 61~5~-~4 5~ from the Llttrow angle rnalntalns 85~ or more for non-polarlzed llght, and the efficiency deviat:lon due to polarization is suf~iciently small to be within 10~. In case that an lncident angle is 5 from the Littrow angle, the angular deviation between the incident angle and the reflection angle of the flrst order diffracted llght corresponds to 10~.
Further as clear ~rom Fig. 14, if a light ls incident from an angle greater than thls, the diffractlon efflciency 14b of the TM wave ls rapldly decreased due to the permittlvity of the surface of dlffraction grating as compared wlth the dlffractlon efficlency 14a of the TE wave. For example, when a llght ls incldent from an angle 10~ Erom the Littrow angle, the deviation of dlffractlon efflclency between both polarizations exceeds 20%, so that the diffraction efflclency 14c for non-polarlzed llght wl 1 1 becorne low.
In Flg. 15, the groove profile of the dlffractlon gratlng used for measurement ls observed by using SEM (Scanning Electron Mlcroscopy). In this case, the groove proflle has a proflle corresponding to condltlons ~uch as r = 0.2, ~/d ~ 1.0 and 2h/d = 0.435. In addltlon, various proflles can be provlded by changlng the comblnatlon of parameters 2h/d, y and ~d. As a result, the inventlon is not llmited to the above-mentloned embodlments.
In Flg. 16, an exposing laser ls indicated at 16a, mirrors are indlcated at 16b, 16c and 16d, a beam s~lltter at 16e, spaclal filters consisting of a lens and pinhole at 16~ and 16g, a photosensitlve layer at 16h and a substrate at 161. The mlrrors , :-:
. .
: - , ~ 3 ~ 195~-14 16c and 16d are dlsposed so that the beams divided into two wlll lnterfere wlth each other on the photosensltlve layer 16h of the substrate 16i.
A coherent llght sent from the exposing laser 16a is reflected by the mlrror 16b and then divld2d lnto two beams through the beam splltter 16e. The beams thus divided are respectively reflected by the mlrrors 16c and 16d to go to the spaclal fllters 16f and 16g thereby to lncrease thelr spacial coherence and to become divergent waves, thus being superimposed to each other on the photosensltlve layer 16h. It ls described, for example, ln E. Wolf, "Progress ln Optlcs XIV", ch. V, pp. 205 (North-Holland 1976) that an lnterference pattern produced by superlmposlng divergent waves on each other generally ls ln the hyperbollc form.
Referrin~ to Fig. 17, when the distance between the pinholes of the spaclal fllters 16f and 16g ls expressed by C, the distance between the middle polnt of the space between the pinholes and the photosensitive layer 16h ls e~pressed by H, and the length of longer side of the substrate 16i ls expressed ~y L, lt ls shown that the rate of the difference of the pattern interval between the interference patterns at the edge portlon of the substrate 161 (dl) and the pattern interval between tho~e at the center portlon thereof (dO), i.e., (dl - dO) /dO, does not exceed 1%. In Flg. 17, the ordinate and abscissa are C/L and H/L, respectlvely. A boundary line 17a lndicates a curve where the ratlo of dlfference becomes 1%, and the shaded area indi.cates the re~ion where lt ls below 1~. The boundary llne 17a satlsfies t'he . ~ ,.
: -. ' followlng condltion: ~ ~ 2 C x H/L2 = 32 As a result, the lnterference pattern to be exposed under the conditlon of C 2 H/L _ 32 can have the pattern interval kept within 1% on the surface of a substrate to be exposed by adopting only a part of the interference patterns of the hyperbollc form as shown ln Fig. 16, so that the interference pattern can be regarded to be llnear. Therefore, there is no need to use any optlcal lnstrument between the spacial fllters and substrate. Thls means that the spaclal coherence is lmproved and interference expo~ure can he achieved by uslng an optical system which is simple ln structure.
In additl~n, slnce the envelope of the lntenslty distributlon on the photosensitive layer 16h is of the Gaussian distrlbutlon, in order to obtain a uniform groove profile all over the substrate in performlng the exposure for a constant period of time, lt ls required that the devlation of the intensity of the envelope o a llght to be exposed all over the substrate be kept wlthin 20% at the central portion where it ls hl~hest and the edge portion where lt ls lowest. For example, when the deviation of exposure lntenslty of an actually produced diffraction grantlng ls 20~, even when non-polarized, a diffractlon efficiency of 80~ or more can be obtained.
As an example of such structure, when settings such as L = 30 mm, H - 600 mm and C = 400 mm are used, and an ob~ective lens with a magniflcatlon of 40 ls used ln the spaclal filter, the dlameter of a beam to be lnterfered on the substrate ls 140 mm, , , . -. .
. :, .
.. ~, . . .
,, :: , :
~32~
the devlation in the envelope of lntenslty distribution on the surface of the photosensitive layer to be exposed ls kept wlthin 10%, the value of C x H~L2 is 260, and the deviation between the interval of the interference patterns at the central and edge portlons of the substrate is kept within 0.1~, which means that no problem arlses practically.
Also, the mirror 16b shown in Fig. 16 can be omltted.
No limitation is ma~e to the above-descrlbed embodlments.
"
. ~ .
... . . : -~
Claims (6)
1. A diffraction grating for diffracting light incident thereupon, comprising:
a substrate;
a photosensitive layer formed on said substrate and having formed on a surface thereof a pattern of cyclic grooves; and a reflection film formed on said surface of said photosensitive layer, wherein said grating has a groove profile .pi.(x) given by:
.pi.(x) = h[sin(Kx) + .gamma.sin(2Kx - 90°)], where a direction perpendicular to the groove is indicated by x-axis, a groove pitch is indicted by d, K = 2.pi./d, and parameters h and .gamma. satisfy the following conditions:
0.26 ? 2h/d ? 0.52 0.05 ? .gamma. ? 0.32, wherein when the wavelength .lambda. of the incident light is normalized with respect to the groove pitch d to a normalized wavelength .lambda./d, the normalized wavelength .lambda./d satisfies the following condition:
0.67 ? .lambda./d ? 1.15, and wherein said grating is used in a mount satisfying the following condition:
.THETA.L - 5° ? .THETA. ? .THETA.L + 5°, where .THETA. denotes the incident angle of the incident light and .THETA.L denotes the first order Littrow angle.
a substrate;
a photosensitive layer formed on said substrate and having formed on a surface thereof a pattern of cyclic grooves; and a reflection film formed on said surface of said photosensitive layer, wherein said grating has a groove profile .pi.(x) given by:
.pi.(x) = h[sin(Kx) + .gamma.sin(2Kx - 90°)], where a direction perpendicular to the groove is indicated by x-axis, a groove pitch is indicted by d, K = 2.pi./d, and parameters h and .gamma. satisfy the following conditions:
0.26 ? 2h/d ? 0.52 0.05 ? .gamma. ? 0.32, wherein when the wavelength .lambda. of the incident light is normalized with respect to the groove pitch d to a normalized wavelength .lambda./d, the normalized wavelength .lambda./d satisfies the following condition:
0.67 ? .lambda./d ? 1.15, and wherein said grating is used in a mount satisfying the following condition:
.THETA.L - 5° ? .THETA. ? .THETA.L + 5°, where .THETA. denotes the incident angle of the incident light and .THETA.L denotes the first order Littrow angle.
2. A diffraction grating for diffracting light incident thereupon, comprising:
a substrate;
a photosensitive layer formed on said substrate and having formed on a surface thereof a pattern of cyclic grooves; and a reflection film formed on said surface of said photosensitive layer, wherein said grating has a groove profile .pi.(x) given by:
.pi.(x) = h[sin(Kx) + .gamma.sin(2Kx - 90°)], where a direction perpendicular to the groove is indicated by x-axis, a groove pitch is indicated by d, K = .pi./d, and parameters h and .gamma. satisfy the following conditions:
0.35 ? 2h/d ? 0.45 0.10 ? .gamma. ? 0.25, wherein when the wavelength .lambda. of the incident light is normalized with respect to the groove pitch d to a normalized wavelength .lambda./d, the normalized wavelength .lambda./d satisfies the following condition:
0.67? .lambda./d ? 1.15, and wherein said grating is used in a mount satisfying the following condition:
.theta.L - 5° ? .theta. ? .theta.L + 5°, where .theta. denotes the incident angle of the incident light and .theta.L denotes the first Littrow angle.
a substrate;
a photosensitive layer formed on said substrate and having formed on a surface thereof a pattern of cyclic grooves; and a reflection film formed on said surface of said photosensitive layer, wherein said grating has a groove profile .pi.(x) given by:
.pi.(x) = h[sin(Kx) + .gamma.sin(2Kx - 90°)], where a direction perpendicular to the groove is indicated by x-axis, a groove pitch is indicated by d, K = .pi./d, and parameters h and .gamma. satisfy the following conditions:
0.35 ? 2h/d ? 0.45 0.10 ? .gamma. ? 0.25, wherein when the wavelength .lambda. of the incident light is normalized with respect to the groove pitch d to a normalized wavelength .lambda./d, the normalized wavelength .lambda./d satisfies the following condition:
0.67? .lambda./d ? 1.15, and wherein said grating is used in a mount satisfying the following condition:
.theta.L - 5° ? .theta. ? .theta.L + 5°, where .theta. denotes the incident angle of the incident light and .theta.L denotes the first Littrow angle.
3. A method of manufacturing a diffraction grating, comprising the steps of:
forming on a substrate a photosensitive layer having a photosensitive characteristic represented by a characteristic curve of an exposure amount versus a film thickness residue of said photosensitive layer after development, said characteristic curve having a region in which the value of the second order differential of said characteristic curve is positive and having no third order inflection point whereby said region can be approximated to a quadratic curve;
subjecting said photosensitive layer to an interference exposure in said region of said characteristic curve; and developing the exposed photosensitive layer to thereby obtain a diffraction grating which has a groove profile .pi.(x), given by:
.pi.(x) = h[sin(Kx) + .gamma.sin(2Kx - 90°)], where a direction perpendicular to the groove is indicated by x-axis, a groove pitch is indicated by d and K = 2.pi./d, wherein when an exposure intensity distribution I(x) is expressed as I(x) = I0 + I1sin(Kx), the following conditions are satisfied:
2h/d = I1¦b + 2aI0¦
.gamma. = aI1/2¦b + 2aI0¦, where a and b respectively denote coefficients of the first and second terms of a formula expressing said quadratic curve.
forming on a substrate a photosensitive layer having a photosensitive characteristic represented by a characteristic curve of an exposure amount versus a film thickness residue of said photosensitive layer after development, said characteristic curve having a region in which the value of the second order differential of said characteristic curve is positive and having no third order inflection point whereby said region can be approximated to a quadratic curve;
subjecting said photosensitive layer to an interference exposure in said region of said characteristic curve; and developing the exposed photosensitive layer to thereby obtain a diffraction grating which has a groove profile .pi.(x), given by:
.pi.(x) = h[sin(Kx) + .gamma.sin(2Kx - 90°)], where a direction perpendicular to the groove is indicated by x-axis, a groove pitch is indicated by d and K = 2.pi./d, wherein when an exposure intensity distribution I(x) is expressed as I(x) = I0 + I1sin(Kx), the following conditions are satisfied:
2h/d = I1¦b + 2aI0¦
.gamma. = aI1/2¦b + 2aI0¦, where a and b respectively denote coefficients of the first and second terms of a formula expressing said quadratic curve.
4. A method as claimed in claim 3, wherein said photosensitive layer is a positive type photoresist, and the following condition is satisfied:
5. A method as claimed in claim 3, wherein said photosensitive layer is a negative type photoresist, and the following conditions are satisfied:
b < O
b < O
6. An apparatus for manufacturing a diffraction grating, comprising:
a laser for producing a light;
a half mirror for dividing the light from said laser into two beams;
two mirrors for respectively reflecting the two beams in directions toward a photosensitive layer formed on a substrate which has a diameter of longitudinal length L; and two spacial filters each including a pinhole for respectively improving the spacial coherences of the reflected two beams from said two mirrors and for converting the reflected two beams to two divergent beams of light so that said photosensitive layer is interferentially exposed by the two divergent beams of light, said two spacial filters be ng spaced from each other by a distance C, and a middle point between the pinholes of said two spacial filters being spaced from said substrate by a distance H, wherein L, C and H satisfy the following condition:
and wherein a deviation of the exposure intensity indicated by an envelope of an exposure intensity distribution on said substrate is within 20%.
a laser for producing a light;
a half mirror for dividing the light from said laser into two beams;
two mirrors for respectively reflecting the two beams in directions toward a photosensitive layer formed on a substrate which has a diameter of longitudinal length L; and two spacial filters each including a pinhole for respectively improving the spacial coherences of the reflected two beams from said two mirrors and for converting the reflected two beams to two divergent beams of light so that said photosensitive layer is interferentially exposed by the two divergent beams of light, said two spacial filters be ng spaced from each other by a distance C, and a middle point between the pinholes of said two spacial filters being spaced from said substrate by a distance H, wherein L, C and H satisfy the following condition:
and wherein a deviation of the exposure intensity indicated by an envelope of an exposure intensity distribution on said substrate is within 20%.
Applications Claiming Priority (4)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP62331972A JPH01172901A (en) | 1987-12-28 | 1987-12-28 | Manufacture of diffraction grating |
| JP62-331978/1987 | 1987-12-28 | ||
| JP62331978A JPH01172902A (en) | 1987-12-28 | 1987-12-28 | Diffraction grating |
| JP62-331972/1987 | 1987-12-28 |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1321495C true CA1321495C (en) | 1993-08-24 |
Family
ID=26574030
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA000587161A Expired - Fee Related CA1321495C (en) | 1987-12-28 | 1988-12-28 | Diffraction grating and manufacturing method thereof |
Country Status (5)
| Country | Link |
|---|---|
| US (1) | US5007709A (en) |
| EP (2) | EP0323238B1 (en) |
| KR (1) | KR920001246B1 (en) |
| CA (1) | CA1321495C (en) |
| DE (1) | DE3855042T2 (en) |
Families Citing this family (28)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5182659A (en) * | 1991-02-20 | 1993-01-26 | Holographix, Inc. | Holographic recording and scanning system and method |
| EP0618473A3 (en) * | 1993-03-31 | 1995-03-15 | Kuraray Co | Video device utilizing a two-dimensional diffraction grating. |
| WO1998006676A1 (en) | 1996-08-13 | 1998-02-19 | Nippon Sheet Glass Co., Ltd. | LASER MACHINING METHOD FOR GlASS SUBSTRATE, DIFFRACTION TYPE OPTICAL DEVICE FABRICATED BY THE MACHINING METHOD, AND METHOD OF MANUFACTURING OPTICAL DEVICE |
| DE19652563A1 (en) | 1996-12-17 | 1998-06-18 | Heidenhain Gmbh Dr Johannes | Photoelectric position measuring device |
| KR20000026880A (en) * | 1998-10-23 | 2000-05-15 | 김영남 | Discontinuous exposure lens using grating and method for fabricating thereof |
| WO2000026703A1 (en) * | 1998-10-30 | 2000-05-11 | Corning Incorporated | Wavelength tuning of photo-induced gratings |
| CA2272008A1 (en) | 1999-05-11 | 2000-11-11 | Francois Trepanier | Device and method for recording an interference pattern in a photosensitive medium |
| US6693745B1 (en) | 1999-09-14 | 2004-02-17 | Corning Incorporated | Athermal and high throughput gratings |
| EP1130422B1 (en) * | 2000-01-18 | 2001-11-21 | Acterna Eningen GmbH | Optical reflection grating, method of optimizing such a grating and optical spectrometer |
| US6577786B1 (en) * | 2000-06-02 | 2003-06-10 | Digital Lightwave, Inc. | Device and method for optical performance monitoring in an optical communications network |
| US20060216478A1 (en) * | 2000-07-26 | 2006-09-28 | Shimadzu Corporation | Grating, negative and replica gratings of the grating, and method of manufacturing the same |
| JP2002098820A (en) * | 2000-09-21 | 2002-04-05 | Nippon Sheet Glass Co Ltd | Reflection type diffraction grating |
| KR100417570B1 (en) * | 2001-08-17 | 2004-02-05 | 손광현 | Reflex reflector having double hologram diffraction grating layers |
| JP4475501B2 (en) * | 2003-10-09 | 2010-06-09 | インターナショナル・ビジネス・マシーンズ・コーポレーション | Spectroscopic element, diffraction grating, composite diffraction grating, color display device, and duplexer |
| DE102004016638A1 (en) * | 2004-03-30 | 2005-10-20 | Zeiss Carl | Diffraction grating for multiplexer or demultiplexer in fibre optic telecommunications cable has a defined grating profile |
| US8233154B2 (en) * | 2005-12-22 | 2012-07-31 | Board Of Supervisors Of Louisiana State University And Agricultural And Mechanical College | High precision code plates and geophones |
| US7677146B2 (en) * | 2006-05-10 | 2010-03-16 | 3M Innovative Properties Company | Cutting tool using one or more machined tool tips in a continuous or interrupted cut fast tool servo |
| US7628100B2 (en) * | 2007-01-05 | 2009-12-08 | 3M Innovative Properties Company | Cutting tool using one or more machined tool tips with diffractive features in a continuous or interrupted cut fast tool servo |
| US7669508B2 (en) * | 2007-10-29 | 2010-03-02 | 3M Innovative Properties Company | Cutting tool using one or more machined tool tips with diffractive features |
| US20090147361A1 (en) * | 2007-12-07 | 2009-06-11 | 3M Innovative Properties Company | Microreplicated films having diffractive features on macro-scale features |
| KR20100134077A (en) * | 2008-04-02 | 2010-12-22 | 쓰리엠 이노베이티브 프로퍼티즈 컴파니 | Methods and systems for fabricating optical films having superimposed features |
| WO2009124107A1 (en) * | 2008-04-02 | 2009-10-08 | 3M Innovative Properties Company | Light directing film and method for making the same |
| EP2422232B1 (en) * | 2009-04-20 | 2017-03-08 | BAE Systems PLC | Surface relief grating in an optical waveguide having a reflecting surface and dielectric layer conforming to the surface |
| CN101718884B (en) * | 2009-11-05 | 2011-05-18 | 中国科学院长春光学精密机械与物理研究所 | Zero-level light optical locating method of optical grating substrate in manufacturing of plane holographic grating |
| DE102012110630A1 (en) * | 2012-11-06 | 2014-05-08 | Ovd Kinegram Ag | Multi-layer body and method for producing a security element |
| WO2019244274A1 (en) * | 2018-06-20 | 2019-12-26 | 株式会社島津製作所 | Device and method for producing master diffraction grating |
| CN108680979A (en) * | 2018-06-21 | 2018-10-19 | 中国人民解放军63908部队 | Two-dimension grating resists Polarization-Sensitive SERS substrates and its processing method |
| CN109164525A (en) * | 2018-10-26 | 2019-01-08 | 上海理工大学 | A kind of holographic concave grating exposure light path of low incisure density |
Family Cites Families (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| AU492267B1 (en) * | 1973-11-13 | 1976-05-13 | Theuniversity Of Tasmania | Diffraction grating |
| GB1506400A (en) * | 1975-12-08 | 1978-04-05 | Rank Organisation Ltd | Diffraction gratings |
| US4402571A (en) * | 1981-02-17 | 1983-09-06 | Polaroid Corporation | Method for producing a surface relief pattern |
| EP0110184B1 (en) * | 1982-11-04 | 1987-03-04 | Sumitomo Electric Industries Limited | Process for fabricating integrated optics |
-
1988
- 1988-12-17 US US07/290,196 patent/US5007709A/en not_active Expired - Lifetime
- 1988-12-28 DE DE3855042T patent/DE3855042T2/en not_active Expired - Fee Related
- 1988-12-28 CA CA000587161A patent/CA1321495C/en not_active Expired - Fee Related
- 1988-12-28 EP EP88312373A patent/EP0323238B1/en not_active Expired - Lifetime
- 1988-12-28 KR KR1019880017677A patent/KR920001246B1/en not_active IP Right Cessation
- 1988-12-28 EP EP95202075A patent/EP0682272A2/en not_active Withdrawn
Also Published As
| Publication number | Publication date |
|---|---|
| DE3855042T2 (en) | 1996-10-02 |
| EP0682272A2 (en) | 1995-11-15 |
| EP0323238A2 (en) | 1989-07-05 |
| EP0323238B1 (en) | 1996-02-28 |
| DE3855042D1 (en) | 1996-04-04 |
| EP0682272A3 (en) | 1995-12-20 |
| US5007709A (en) | 1991-04-16 |
| EP0323238A3 (en) | 1990-12-19 |
| KR890010590A (en) | 1989-08-09 |
| KR920001246B1 (en) | 1992-02-08 |
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